**3.4 Reasons for the fan-mechanism operation at high σ3 and new strength profiles for hard rocks**

**Figure 10** illustrates the evolution of failure mechanisms in hard rock specimens with rising σ3. Confining pressure σ3 increases along the horizontal axis from left to right. At the origin of the horizontal axis, σ3 = 0. The basic point is that the failure process of brittle rocks at any level of σ3 is accompanied by formation of tensile cracks; however, the ultimate length ℓ of tensile cracks that can be developed at failure depends on the level of σ3 because rising σ3 suppresses the tensile crack growth. A dotted curve here shows symbolically the typical variation of ultimate length ℓ of tensile cracks as a function of σ3: the higher the σ3, the shorter the ℓ. The length ℓ of tensile cracks in turn determines the macroscopic failure mechanism and the failure pattern shown schematically in rock specimens (i)–(iv).

Within the pressure range 0 ≤ σ3 < σ3shear, shear rupture cannot propagate in its own plane due to creation at the rupture tip of relatively long tensile cracks that prevent the shear rupture propagation. The following two basic principles of the failure process taking place within this pressure range may be distinguished:

i.Splitting by long tensile cracks (at low σ3)

ii.Distributed microcracking followed by coalescence of microcracks (at larger σ3)

At σ<sup>3</sup> ≥ σ3shear the failure mode is localised shear. Here high enough confining pressure σ3 suppresses the formation of long tensile cracks, and tensile cracks generated in the rupture tip become sufficiently short to assist shear rupture to propagate in its own plane. The fracture front moves through the rock due to creation of an echelon of micro-tensile cracks in the fracture tip and inter-crack slabs (domino blocks) which are subjected to rotation at shear displacement of the rupture faces. Here, depending on behaviour of domino blocks at rotation, two basic principles of the failure process may be distinguished as discussed in **Figure 4**:


An important fact is that the fan mechanism exhibits different efficiency depending on the level of σ3. We will determine the fan-mechanism efficiency as the ratio between the frictional strength and the fan strength: ψ = τf/τfan. The point is that the length r of domino blocks decreases with rising σ3. At confining pressure near σ3fan(min), when the relative length (r/w) of domino blocks is still relatively large, the blocks are subject to partial destruction as they rotate. In this case the fanmechanism efficiency is quite low. At higher σ3, with shorter blocks, this imperfection decreases, rendering the fan mechanism more efficient. The optimal efficiency takes place at σ3fan(opt) when the blocks with an optimal ratio r/w rotate with minimum destruction. At greater σ3 the efficiency reduces because shorter blocks gradually lose their potential for operation as hinges. Finally very short blocks lose this capability completely, and the rock behaviour returns to the conventional frictional mode. This happens at σ3fan(max). The green curve in **Figure 10** illustrates

**73**

confining stress σ3.

*rock brittleness variation with rising σ3.*

**Figure 11.**

the situation where σ3 < σ3 fan(opt).

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic…*

graphically a possible variation of the fan-mechanism efficiency ψ = τf/τfan versus

*Strength profiles and brittleness profiles for hard rocks. a), b) and c) Strength profiles for τs, τf and τfan plotted on the basis of complete stress-strain curves. d) Difference between the conventional and new understanding of* 

The variable efficiency of the fan mechanism with σ3 causes corresponding variation in the transient strength and brittleness of hard rocks. **Figure 11a** shows schematically an improved model of strength profiles involving conventional fracture τs and frictional τf strength profiles and the transient fan strength τfan profile (red curve). Stress-displacement curves in **Figure 11b** and **c** reflecting real post-peak rock properties (shown in red) explain the meaning of the fan strength profile and its variation versus σ3. **Figure 11b** corresponds to the situation at σ3 = σ3fan(opt) where the fan mechanism exhibits the maximum efficiency. At peak stress the material strength is τs. After completion of the fan structure, the specimen strength decreases to the level τfan representing the transient material strength. This means that the shear fracture governed by the fan mechanism can propagate through the material at any level of shear stress above τfan. After the fan has crossed the specimen body, the specimen strength is determined by the frictional strength τf of the new fault. For confining pressures σ3 < σ3 fan(opt) or σ3 > σ3 fan(opt) the fan-mechanism efficiency is lower. The graph in **Figure 11c** indicates the relative values of τs, τf and τfan and their positions on the profiles for

Let us analyse how the variable efficiency of the fan mechanism can affect the rock brittleness. In the simplest case, the brittleness of the same rock for different testing conditions can be estimated as the reciprocal of the specific rupture energy associated with the rupture propagation governed by the fan mechanism through

*DOI: http://dx.doi.org/10.5772/intechopen.85413*

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic… DOI: http://dx.doi.org/10.5772/intechopen.85413*

#### **Figure 11.**

*Earth Crust*

observed for extreme ruptures [6, 13].

pattern shown schematically in rock specimens (i)–(iv).

i.Splitting by long tensile cracks (at low σ3)

the failure process may be distinguished as discussed in **Figure 4**:

standing rotation without collapse (at σ3 > σ3fan(min))

blocks (at σ3shear ≤ σ<sup>3</sup> ≤ σ3fan(min))

**profiles for hard rocks**

is discussed in [19, 20]. The fan mechanism explains also the heat flow paradox

**3.4 Reasons for the fan-mechanism operation at high σ3 and new strength** 

**Figure 10** illustrates the evolution of failure mechanisms in hard rock specimens with rising σ3. Confining pressure σ3 increases along the horizontal axis from left to right. At the origin of the horizontal axis, σ3 = 0. The basic point is that the failure process of brittle rocks at any level of σ3 is accompanied by formation of tensile cracks; however, the ultimate length ℓ of tensile cracks that can be developed at failure depends on the level of σ3 because rising σ3 suppresses the tensile crack growth. A dotted curve here shows symbolically the typical variation of ultimate length ℓ of tensile cracks as a function of σ3: the higher the σ3, the shorter the ℓ. The length ℓ of tensile cracks in turn determines the macroscopic failure mechanism and the failure

Within the pressure range 0 ≤ σ3 < σ3shear, shear rupture cannot propagate in its own plane due to creation at the rupture tip of relatively long tensile cracks that prevent the shear rupture propagation. The following two basic principles of the failure process taking place within this pressure range may be distinguished:

ii.Distributed microcracking followed by coalescence of microcracks (at larger σ3)

At σ<sup>3</sup> ≥ σ3shear the failure mode is localised shear. Here high enough confining pressure σ3 suppresses the formation of long tensile cracks, and tensile cracks generated in the rupture tip become sufficiently short to assist shear rupture to propagate in its own plane. The fracture front moves through the rock due to creation of an echelon of micro-tensile cracks in the fracture tip and inter-crack slabs (domino blocks) which are subjected to rotation at shear displacement of the rupture faces. Here, depending on behaviour of domino blocks at rotation, two basic principles of

iii.Frictional shear—characterised by collapse of insufficiently short domino

iv.Fan-hinged shear—associated with formation of the fan structure consisting of sufficiently short domino blocks (of length r = ℓ and width w) and with-

An important fact is that the fan mechanism exhibits different efficiency depending on the level of σ3. We will determine the fan-mechanism efficiency as the ratio between the frictional strength and the fan strength: ψ = τf/τfan. The point is that the length r of domino blocks decreases with rising σ3. At confining pressure near σ3fan(min), when the relative length (r/w) of domino blocks is still relatively large, the blocks are subject to partial destruction as they rotate. In this case the fanmechanism efficiency is quite low. At higher σ3, with shorter blocks, this imperfection decreases, rendering the fan mechanism more efficient. The optimal efficiency

takes place at σ3fan(opt) when the blocks with an optimal ratio r/w rotate with minimum destruction. At greater σ3 the efficiency reduces because shorter blocks gradually lose their potential for operation as hinges. Finally very short blocks lose this capability completely, and the rock behaviour returns to the conventional frictional mode. This happens at σ3fan(max). The green curve in **Figure 10** illustrates

**72**

*Strength profiles and brittleness profiles for hard rocks. a), b) and c) Strength profiles for τs, τf and τfan plotted on the basis of complete stress-strain curves. d) Difference between the conventional and new understanding of rock brittleness variation with rising σ3.*

graphically a possible variation of the fan-mechanism efficiency ψ = τf/τfan versus confining stress σ3.

The variable efficiency of the fan mechanism with σ3 causes corresponding variation in the transient strength and brittleness of hard rocks. **Figure 11a** shows schematically an improved model of strength profiles involving conventional fracture τs and frictional τf strength profiles and the transient fan strength τfan profile (red curve). Stress-displacement curves in **Figure 11b** and **c** reflecting real post-peak rock properties (shown in red) explain the meaning of the fan strength profile and its variation versus σ3. **Figure 11b** corresponds to the situation at σ3 = σ3fan(opt) where the fan mechanism exhibits the maximum efficiency. At peak stress the material strength is τs. After completion of the fan structure, the specimen strength decreases to the level τfan representing the transient material strength. This means that the shear fracture governed by the fan mechanism can propagate through the material at any level of shear stress above τfan. After the fan has crossed the specimen body, the specimen strength is determined by the frictional strength τf of the new fault. For confining pressures σ3 < σ3 fan(opt) or σ3 > σ3 fan(opt) the fan-mechanism efficiency is lower. The graph in **Figure 11c** indicates the relative values of τs, τf and τfan and their positions on the profiles for the situation where σ3 < σ3 fan(opt).

Let us analyse how the variable efficiency of the fan mechanism can affect the rock brittleness. In the simplest case, the brittleness of the same rock for different testing conditions can be estimated as the reciprocal of the specific rupture energy associated with the rupture propagation governed by the fan mechanism through

**Figure 12.**

*(a) Variation of the fan-mechanism efficiency ψ = τf/τfan versus confining pressure σ3 for rocks of different hardness (UCS). (b) Variation of the optimal efficiency of the fan mechanism ψopt versus UCS.*

#### **Figure 13.**

*a) Shear rupture propagation by advanced triggering of new segments (modified photograph from [29]). b) and c) Principle of formation of the domino and fan structure in segmented faults.*

**75**

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic…*

intact rock. Shaded areas on stress-strain curves in **Figure 11b** and **c** represent the specific rupture energy Wr for different σ3. The brittleness index K = 1/Wr can be used to characterise the brittleness variation versus σ3. The shaded line in **Figure 11d** illustrates symbolically the conventional understanding of rock brittleness variation in accordance with which the rising confining pressures σ3 make rock less brittle. Because the fan mechanism decreases dramatically the specific rupture energy within the pressure range σ3fan(min) < σ3 < σ3fan(max), the brittleness at these stress conditions should be significantly higher than the conventional understanding. The blue curve in **Figure 11d** indicates the character of rock embrittlement caused by the fan mechanism. Estimations made in [17, 22] show that at high σ3 rock brittleness can be a hundred of times higher than at low σ3. At σ3 = σ3fan(opt) rock conditions can be

The fan-mechanism efficiency ψ = τf/τfan depends also on the rock hardness characterised by UCS. **Figure 12a** shows three curves indicating variations of ψ = τf/τfan versus σ3 for three rocks of different hardness. Here the harder the rock, the greater the optimal fan-mechanism efficiency ψopt and the larger the range of σ3 where the fan mechanism is active. The red curve in **Figure 12b** illustrates symbolically the dependence of the optimal efficiency of the fan mechanism ψopt on the hardness (UCS) of different rocks. The fan mechanism operates with the largest efficiency in rocks with UCS > 250 MPa. Within the range of UCS 150–250 (roughly), the efficiency is significantly lower. In soft rocks the fan mechanism is

**4. Fan mechanism as a source of dynamic events in the earth's crust**

This section discusses the role of the fan mechanism in generation of shallow earthquakes and shear rupture rockbursts in deep mines. In the previous sections, we introduced different unique features of the fan mechanism and 'abnormal' properties of hard rocks. All analysis was conducted for primary shear ruptures which are thin and continuous. Unlike primary ruptures natural faults typically have very complicated segmented and multi-hierarchical structure [7, 33, 34]. Main principles of the complex fault evolution in association with the fan mechanism were discussed in [20, 23, 35]. Here we will outline briefly most important features

It was observed that in ultra-deep South African mines, very severe dynamic events (shear rupture rockbursts) are caused by new shear ruptures generated in pristine rock [36, 37]. These mine tremors are seismically indistinguishable from natural earthquakes and share the apparent paradox of failure under low shear stress [37]. Photographs of such faults are shown in **Figure 5b**. The structure of all these faults is identical consisting of a row of domino blocks. However, the domino

**Figure 13** explains features of this structure formation. Series of photographs in **Figure 13a** (modified from [38]) shows principles of segmented fault propagation observed experimentally. The fault propagates due to advanced triggering of new segments. The photographs show four stages (I–IV) of the fault evolution. Segments are represented here by white lines. The fault propagates from left to right. The segments are generated one by one due to the stress transfer and propagate bilaterally. At the meeting of each two neighbouring segments, they are connected by a compressive jog. It was found out in [29, 38] that jogs of the compression type are very common at high confining pressures to fault zones regardless of their sizes. Overlap zones of the jogs

**4.1 Features of the fan-structure formation in complex natural faults**

of the fan-mechanism generation in complex faults.

structure is more complex than in primary ruptures.

*DOI: http://dx.doi.org/10.5772/intechopen.85413*

super brittle.

not active.

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic… DOI: http://dx.doi.org/10.5772/intechopen.85413*

intact rock. Shaded areas on stress-strain curves in **Figure 11b** and **c** represent the specific rupture energy Wr for different σ3. The brittleness index K = 1/Wr can be used to characterise the brittleness variation versus σ3. The shaded line in **Figure 11d** illustrates symbolically the conventional understanding of rock brittleness variation in accordance with which the rising confining pressures σ3 make rock less brittle. Because the fan mechanism decreases dramatically the specific rupture energy within the pressure range σ3fan(min) < σ3 < σ3fan(max), the brittleness at these stress conditions should be significantly higher than the conventional understanding. The blue curve in **Figure 11d** indicates the character of rock embrittlement caused by the fan mechanism. Estimations made in [17, 22] show that at high σ3 rock brittleness can be a hundred of times higher than at low σ3. At σ3 = σ3fan(opt) rock conditions can be super brittle.

The fan-mechanism efficiency ψ = τf/τfan depends also on the rock hardness characterised by UCS. **Figure 12a** shows three curves indicating variations of ψ = τf/τfan versus σ3 for three rocks of different hardness. Here the harder the rock, the greater the optimal fan-mechanism efficiency ψopt and the larger the range of σ3 where the fan mechanism is active. The red curve in **Figure 12b** illustrates symbolically the dependence of the optimal efficiency of the fan mechanism ψopt on the hardness (UCS) of different rocks. The fan mechanism operates with the largest efficiency in rocks with UCS > 250 MPa. Within the range of UCS 150–250 (roughly), the efficiency is significantly lower. In soft rocks the fan mechanism is not active.
